Dynamizing Succinct Tree Representations

We consider succinct, or space-efficient, representations of ordinal trees. Representations exist that take 2n+o(n) bits to represent a staticn-node ordinal tree --- close to the information-theoretic minimum --- and support navigational operations in O(1) time on a RAM model; and some implementations have good practical performance. The situation is different for dynamic ordinal trees. Although there is theoretical work on succinct dynamic ordinal trees, there is little work on the practical performance of these data structures. Motivated by applications to representing XML documents, in this paper, we report on a preliminary study on dynamic succinct data structures. Our implementation is based on representing the tree structure as a sequence of balanced parentheses, with navigation done using the min-max tree of Sadakane and Navarro (SODA '10). Our implementation shows promising performance for update and navigation, and our findings highlight two issues that we believe will be important to future implementations: the difference between the finger model of (say) Farzan and Munro (ICALP '09) and the parenthesis model of Sadakane and Navarro, and the choice of the balanced tree used to represent the min-max tree.

[1]  Rajeev Raman,et al.  Succinct Dynamic Dictionaries and Trees , 2003, ICALP.

[2]  Gonzalo Navarro,et al.  Fast in-memory XPath search using compressed indexes , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[3]  S. Srinivasa Rao,et al.  Succinct Representation of Data Structures , 2018, Handbook of Data Structures and Applications.

[4]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[5]  Michael E. Saks,et al.  The cell probe complexity of dynamic data structures , 1989, STOC '89.

[6]  Gonzalo Navarro,et al.  Succinct Trees in Practice , 2010, ALENEX.

[7]  Guy Jacobson,et al.  Space-efficient static trees and graphs , 1989, 30th Annual Symposium on Foundations of Computer Science.

[8]  Rajeev Raman,et al.  Succinct ordinal trees with level-ancestor queries , 2004, SODA '04.

[9]  Naila Rahman,et al.  Engineering the LOUDS Succinct Tree Representation , 2006, WEA.

[10]  Naila Rahman,et al.  Engineering succinct DOM , 2008, EDBT '08.

[11]  Ioana Manolescu,et al.  XMark: A Benchmark for XML Data Management , 2002, VLDB.

[12]  S. Srinivasa Rao,et al.  Succinct Representations of Functions , 2004, ICALP.

[13]  Venkatesh Raman,et al.  Representing dynamic binary trees succinctly , 2001, SODA '01.

[14]  Wing-Kai Hon,et al.  Compressed indexes for dynamic text collections , 2007, TALG.

[15]  Rajeev Raman,et al.  Representing Trees of Higher Degree , 2005, Algorithmica.

[16]  Sartaj Sahni,et al.  Handbook of Data Structures and Applications , 2004 .

[17]  Richard Cole,et al.  A unified access bound on comparison-based dynamic dictionaries , 2007, Theor. Comput. Sci..

[18]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[19]  Naila Rahman,et al.  A simple optimal representation for balanced parentheses , 2006, Theor. Comput. Sci..

[20]  J. Ian Munro,et al.  Succinct Representation of Balanced Parentheses and Static Trees , 2002, SIAM J. Comput..

[21]  Gonzalo Navarro,et al.  Fully-functional succinct trees , 2010, SODA '10.

[22]  Raymond K. Wong,et al.  Querying and maintaining a compact XML storage , 2007, WWW '07.

[23]  J. Ian Munro,et al.  Succinct representation of dynamic trees , 2011, Theor. Comput. Sci..

[24]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[25]  Sartaj Sahni,et al.  Handbook Of Data Structures And Applications (Chapman & Hall/Crc Computer and Information Science Series.) , 2004 .